Detailed Description

template<class T>
class gismo::gsALMBase< T >

Performs the arc length method to solve a nonlinear system of equations.

Template Parameters

T	coefficient type

Inheritance diagram for gsALMBase< T >:

Collaboration diagram for gsALMBase< T >:

Public Member Functions
virtual void	applyOptions ()
	Apply the options.

virtual gsStatus	computeSingularPoint (const gsVector< T > &U, const T &L, bool switchBranch=false, bool jacobian=false, bool testPoint=true)
	Calculates the singular point. More...

virtual gsStatus	computeStability (bool jacobian=true, T shift=-1e2)
	Calculates the stability of the solution x. More...

virtual bool	converged () const
	True if the Arc Length method converged.

	gsALMBase (const Jacobian_t &Jacobian, const ALResidual_t &ALResidual, const gsVector< T > &Force)
	Constructor.

	gsALMBase (const dJacobian_t &dJacobian, const ALResidual_t &Residual, const gsVector< T > &Force)
	Constructor using the jacobian that takes the solution and the solution step.

virtual T	indicator () const
	Returns the value of the Determinant or other indicator.

virtual void	initialize (bool stability=true)
	Initialize the arc-length method, computes the stability of the initial configuration if stability is true.

virtual bool	isBifurcation (bool jacobian=false)
	Returns true if the point is a bifurcation.

virtual bool	isStable () const
	Returns if solution passed a bifurcation point.

virtual index_t	numIterations () const
	Returns the number of Newton iterations performed.

virtual gsOptionList &	options ()
	Access the options.

virtual const void	options_into (gsOptionList options)
	Return the options into options.

virtual T	reduceLength (T fac=0.5)
	Reduce the length by multiplication with a factor fac.

virtual T	resetLength ()
	Reset the length.

virtual void	resetStep ()
	Resets the step.

virtual T	residue () const
	Returns the error after solving the nonlinear system.

virtual void	setLength (T length)
	Set arc length to length.

virtual void	setLength (T length, bool adaptive)
	Set arc length to length, enables adaptive steps.

virtual void	setLength (T length, bool adaptive, index_t iterations)
	Set arc length to length, enables adaptive steps aiming for iterations number of iterations per step.

virtual void	setLength (T length, index_t iterations)
	Set arc length to length, enables adaptive steps aiming for iterations number of iterations per step.

virtual void	setOptions (gsOptionList options)
	Set the options to options.

virtual void	setSolution (const gsVector< T > &U, const T &L)
	Sets the solution.

virtual void	setSolutionStep (const gsVector< T > &DU, const T &DL)
	Sets the solution step.

virtual const gsVector< T > &	solutionU () const
	Return the solution vector and factor.

virtual index_t	stability () const
	Computes the stability: -1 if unstable, +1 if stable.

virtual bool	stabilityChange () const
	Checks if the stability of the system changed since the previously known solution.

virtual gsStatus	step ()
	Perform one arc-length step.

virtual void	switchBranch ()
	Switches branches.

virtual T	tolerance () const
	Returns the tolerance value used.

Protected Member Functions
virtual index_t	_bisectionObjectiveFunction (const gsVector< T > &x, bool jacobian=true)
	Returns the objective function for the bisection method given solution x.

virtual bool	_bisectionSolve (const gsVector< T > &U, const T L, const T tol)
	Perform a bisection system solve to find a singular point.

virtual T	_bisectionTerminationFunction (const gsVector< T > &x, bool jacobian=true)
	Returns the termination function for the bisection method given solution x.

virtual gsSparseMatrix< T >	_computeJacobian (const gsVector< T > &U, const gsVector< T > &dU)
	Compute the jacobian matrix.

virtual void	_computeSingularPoint (const gsVector< T > &U, const T &L, bool switchBranch=false, bool jacobian=false, bool testPoint=true)
	See computeSingularPoint.

virtual void	_computeStability (const gsVector< T > &x, bool jacobian=true, T shift=-1e2)
	See computeStability.

virtual void	_extendedSystemIteration ()
	Perform an extended system iteration.

virtual bool	_extendedSystemSolve (const gsVector< T > &U, const T L, const T tol)
	Perform an extended system solve to find a singular point.

virtual void	_initOutputExtended ()
	Initialize the output for extended iterations.

virtual void	_step ()
	Implementation of step.

virtual void	_stepOutputExtended ()
	Step output for extended iterations.

virtual bool	_testSingularPoint (bool jacobian=false)
	Tests if a point is a bifurcation point. More...

virtual void	computeLength ()
	Compute the adaptive arc-length.

virtual gsVector< T >	computeResidual (const gsVector< T > &U, const T &L)
	Compute the residual.

virtual void	computeResidualNorms ()
	Compute the residual error norms.

virtual void	computeUbar ()
	Compute \(\bar_u\).

virtual void	computeUt ()
	Compute \(\u_t\).

virtual void	defaultOptions ()
	Set default options.

virtual void	factorizeMatrix (const gsSparseMatrix< T > &M)
	Factorize the matrix M.

virtual void	getOptions ()
	Apply options.

virtual void	init (bool stability)
	Initialize the solver.

virtual void	initiateStep ()=0
	Initiate the first iteration.

virtual void	initMethods ()=0
	Initialize the ALM.

virtual void	initOutput ()=0
	Initialize the output.

virtual void	iteration ()=0
	A single iteration.

virtual void	iterationFinish ()=0
	Finish the iterations.

virtual void	predictor ()=0
	Step predictor.

virtual void	quasiNewtonIteration ()=0
	Perform iteration using quasi-newton method.

virtual void	quasiNewtonPredictor ()=0
	Provide a specialized predictor when using quasi newton methods.

virtual gsVector< T >	solveSystem (const gsVector< T > &F)
	Solve the system with right-hand side F.

virtual void	stepOutput ()=0
	Provide step-wise output.

Protected Attributes
T	m_arcLength
	Length of the step in the u,f plane.

bool	m_converged
	Convergence result.

T	m_DeltaL
	Update of lambdaGeneralizedSelfAdjointEigenSolver.

T	m_deltaL
	Update of update of lambda.

gsVector< T >	m_deltaLs
	Vector with lambda updates.

gsVector< T >	m_DeltaU
	Update of displacement vector.

gsVector< T >	m_deltaU
	Update of update of displacement vector.

gsVector< T >	m_deltaUbar
	u_bar

gsVector< T >	m_deltaUt
	u_t

index_t	m_desiredIterations
	Number of desired iterations.

T	m_indicator
	Indicator for bifurcation.

gsSparseMatrix< T >	m_jacMat
	Jacobian matrix.

T	m_L
	Lambda (present, at previously converged point)

index_t	m_maxIterations
	Maximum number of Arc Length iterations allowed.

index_t	m_numIterations
	Number of Arc Length iterations performed.

T	m_relax
	Relaxation factor.

T	m_residue
	Force residuum.

T	m_residueF
	Force residuum.

T	m_residueKTPhi
	Singular point.

T	m_residueL
	Load residuum.

T	m_residueU
	Displacement residuum.

gsVector< T >	m_resVec
	Value of residual function.

T	m_tolerance
	Tolerance value to decide convergence.

T	m_toleranceF
	Tolerance value to decide convergence - Force criterion.

T	m_toleranceU
	Tolerance value to decide convergence - Displacement criterion.

gsVector< T >	m_U
	Displacement vector (present, at previously converged point)

Member Function Documentation

bool _testSingularPoint ( bool jacobian = false )

protectedvirtual

Tests if a point is a bifurcation point.

Parameters

[in] jacobian Evaluate the Jacobian?

Returns: True if it is a bifurcation point

gsStatus computeSingularPoint	(	const gsVector< T > &	U,
		const T &	L,
		bool	switchBranch = `false`,
		bool	jacobian = `false`,
		bool	testPoint = `true`
	)

virtual

Calculates the singular point.

Parameters

[in]	singTol	The tolerance for convergence
[in]	kmax	The maximum number of iterations for the initial power method
[in]	U	The point to start (displacements)
[in]	L	The point to start (loads)
[in]	tolE	The tolerance for the extended iterations
[in]	tolB	The tolerance for the bisection method
[in]	switchBranch	Switches branch if true
[in]	jacobian	Evaluate the Jacobian?

gsStatus computeStability	(	bool	jacobian = `true`,
		T	shift = `-1e2`
	)

virtual

Calculates the stability of the solution x.

note; The shift is needed to ensure that a negative eigenvalue is found

Parameters

[in]	x	Solution vector
[in]	jacobian	Compute the jacobian?
[in]	shift	The shift to apply

Detailed Description

template<class T> class gismo::gsALMBase< T >

Public Member Functions

Protected Member Functions

Protected Attributes

Member Function Documentation

template<class T>
class gismo::gsALMBase< T >